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There are exactly 3 ways to add 4 odd numbers to get 10. Find all the ways of adding 8 odd numbers to get 20. To be sure of getting all the solutions you will need to be systematic. What about a total of 15 with 6 odd numbers?

Weekly Problem 43 - 2010

Stage: 3 Short Challenge Level: Challenge Level:1

In each of the squares in the grid, one of the letters P, Q, R and S must be entered in such a way that touching squares (whether connected by an edge or just a corner) do not contain the same letter. Some of the letters have alread been entered as shown.

What are the possibilities for the letter in the shaded square?

If you liked this problem, here is an NRICH task which challenges you to use similar mathematical ideas.


This problem is taken from the UKMT Mathematical Challenges.

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